# Parallel Time Integration for NSEMSolver.jl
# Synchronized time stepping with communication/computation overlap

using LinearAlgebra

"""
    ParallelTimeIntegrator

Abstract base type for parallel time integration schemes.
"""
abstract type ParallelTimeIntegrator end

"""
    ParallelRungeKutta

Parallel Runge-Kutta time integrator with communication optimization.
"""
struct ParallelRungeKutta <: ParallelTimeIntegrator
    butcher_tableau::Any                    # Butcher tableau for RK method
    order::Int                              # Order of accuracy
    num_stages::Int                         # Number of RK stages
    
    # Parallel-specific parameters
    pdomain::ParallelDomain
    comm_pattern::CommunicationPattern
    
    # Working storage
    stage_vectors::Vector{DistributedVector}  # Stage vectors k_i
    temp_solution::DistributedVector          # Temporary solution storage
    
    # Time step synchronization
    dt_local::Float64                        # Local stable time step
    dt_global::Float64                       # Global synchronized time step
    
    # Performance tracking
    comm_overlap_efficiency::Float64         # Communication/computation overlap efficiency
    timer::ParallelTimer
end

"""
    create_parallel_rk4(pdomain::ParallelDomain, n_local::Int) -> ParallelRungeKutta

Create parallel 4th-order Runge-Kutta integrator.
"""
function create_parallel_rk4(pdomain::ParallelDomain, n_local::Int)
    # Standard RK4 Butcher tableau
    butcher_tableau = (
        c = [0.0, 0.5, 0.5, 1.0],
        a = [
            [0.0, 0.0, 0.0, 0.0],
            [0.5, 0.0, 0.0, 0.0],
            [0.0, 0.5, 0.0, 0.0],
            [0.0, 0.0, 1.0, 0.0]
        ],
        b = [1.0/6.0, 1.0/3.0, 1.0/3.0, 1.0/6.0]
    )
    
    # Create communication pattern
    comm_pattern = create_communication_pattern(pdomain)
    
    # Initialize working storage
    stage_vectors = [create_distributed_vector(zeros(Float64, n_local), pdomain) for _ in 1:4]
    temp_solution = create_distributed_vector(zeros(Float64, n_local), pdomain)
    
    # Initialize timing
    timer = create_parallel_timer(pdomain.mpi_ctx)
    
    return ParallelRungeKutta(
        butcher_tableau, 4, 4, pdomain, comm_pattern,
        stage_vectors, temp_solution, 0.0, 0.0, 0.0, timer
    )
end

"""
    parallel_timestep!(integrator::ParallelRungeKutta, u::DistributedVector, 
                      rhs_function, dt::Float64, t::Float64) -> Float64

Perform one parallel time step with optimized communication.
"""
function parallel_timestep!(integrator::ParallelRungeKutta, u::DistributedVector,
                           rhs_function, dt::Float64, t::Float64)
    
    start_timer!(integrator.timer, "total_timestep")
    
    # Synchronize time step across all processes
    dt_sync = synchronize_timestep(integrator, dt)
    
    butcher = integrator.butcher_tableau
    
    # Clear stage vectors
    for k in integrator.stage_vectors
        fill!(k.local_values, 0.0)
    end
    
    # Runge-Kutta stages with communication overlap
    for stage in 1:integrator.num_stages
        start_timer!(integrator.timer, "stage_$stage")
        
        # Compute intermediate solution
        integrator.temp_solution.local_values .= u.local_values
        for prev_stage in 1:stage-1
            if butcher.a[stage][prev_stage] != 0.0
                axpy!(dt_sync * butcher.a[stage][prev_stage], 
                      integrator.stage_vectors[prev_stage].local_values,
                      integrator.temp_solution.local_values)
            end
        end
        
        # Exchange ghost values with computation overlap
        start_timer!(integrator.timer, "communication")
        
        function compute_interior_rhs()
            # Compute RHS for interior points (those not needing ghost data)
            interior_indices = get_interior_indices(integrator.pdomain)
            if !isempty(interior_indices)
                compute_rhs_subset!(integrator.stage_vectors[stage], rhs_function,
                                  integrator.temp_solution, t + butcher.c[stage] * dt_sync,
                                  interior_indices)
            end
        end
        
        # Overlap communication with interior computation
        exchange_ghost_values_with_overlap!(
            integrator.temp_solution.local_values, 
            integrator.temp_solution.local_values,  # Dummy for v component
            integrator.temp_solution.local_values,  # Dummy for p component
            integrator.pdomain, integrator.comm_pattern, compute_interior_rhs
        )
        
        stop_timer!(integrator.timer, "communication")
        
        # Compute RHS for boundary points (those needing ghost data)
        start_timer!(integrator.timer, "boundary_rhs")
        boundary_indices = get_boundary_indices(integrator.pdomain)
        if !isempty(boundary_indices)
            compute_rhs_subset!(integrator.stage_vectors[stage], rhs_function,
                              integrator.temp_solution, t + butcher.c[stage] * dt_sync,
                              boundary_indices)
        end
        stop_timer!(integrator.timer, "boundary_rhs")
        
        stop_timer!(integrator.timer, "stage_$stage")
    end
    
    # Combine stages to get final result
    start_timer!(integrator.timer, "final_combination")
    for stage in 1:integrator.num_stages
        if butcher.b[stage] != 0.0
            axpy!(dt_sync * butcher.b[stage], 
                  integrator.stage_vectors[stage].local_values, u.local_values)
        end
    end
    stop_timer!(integrator.timer, "final_combination")
    
    stop_timer!(integrator.timer, "total_timestep")
    
    return dt_sync
end

"""
    synchronize_timestep(integrator::ParallelRungeKutta, dt_local::Float64) -> Float64

Synchronize time step across all processes for stability.
"""
function synchronize_timestep(integrator::ParallelRungeKutta, dt_local::Float64)
    # Use the minimum time step across all processes for stability
    dt_global = all_reduce_scalar(dt_local, min, integrator.pdomain.mpi_ctx)
    
    integrator.dt_local = dt_local
    integrator.dt_global = dt_global
    
    return dt_global
end

"""
    get_interior_indices(pdomain::ParallelDomain) -> Vector{Int}

Get indices of interior points that don't need ghost data for RHS computation.
"""
function get_interior_indices(pdomain::ParallelDomain)
    # Simplified - would identify points away from processor boundaries
    n_local = pdomain.local_domain.n_block^pdomain.local_domain.dim
    overlap_thickness = 2  # Points near boundary that might need ghost data
    
    interior_indices = Int[]
    # This is a simplified implementation - real version would consider domain geometry
    for i in overlap_thickness+1:n_local-overlap_thickness
        push!(interior_indices, i)
    end
    
    return interior_indices
end

"""
    get_boundary_indices(pdomain::ParallelDomain) -> Vector{Int}

Get indices of boundary points that need ghost data for RHS computation.
"""
function get_boundary_indices(pdomain::ParallelDomain)
    # Simplified - would identify points near processor boundaries
    n_local = pdomain.local_domain.n_block^pdomain.local_domain.dim
    overlap_thickness = 2
    
    boundary_indices = Int[]
    # Add points near boundaries
    for i in 1:overlap_thickness
        push!(boundary_indices, i)
    end
    for i in n_local-overlap_thickness+1:n_local
        push!(boundary_indices, i)
    end
    
    return boundary_indices
end

"""
    compute_rhs_subset!(k::DistributedVector, rhs_function, u::DistributedVector,
                       t::Float64, indices::Vector{Int})

Compute RHS for a subset of points specified by indices.
"""
function compute_rhs_subset!(k::DistributedVector, rhs_function, u::DistributedVector,
                           t::Float64, indices::Vector{Int})
    # This would call the RHS function for only the specified indices
    # Simplified implementation - real version would be more sophisticated
    
    if !isempty(indices)
        # Compute full RHS and extract subset (inefficient but functional)
        full_rhs = similar(u.local_values)
        rhs_function(full_rhs, u.local_values, t)
        
        for idx in indices
            k.local_values[idx] = full_rhs[idx]
        end
    end
end

"""
    ParallelIMEX

Parallel Implicit-Explicit (IMEX) time integrator for stiff problems.
"""
struct ParallelIMEX <: ParallelTimeIntegrator
    explicit_integrator::ParallelRungeKutta    # For non-stiff terms
    implicit_solver::ParallelKrylovSolver      # For stiff terms
    
    pdomain::ParallelDomain
    
    # IMEX-specific storage
    explicit_rhs::DistributedVector
    implicit_rhs::DistributedVector
    implicit_matrix::DistributedNSMatrix
    
    # Performance tracking
    timer::ParallelTimer
end

"""
    create_parallel_imex(pdomain::ParallelDomain, n_local::Int,
                        implicit_matrix::DistributedNSMatrix) -> ParallelIMEX

Create parallel IMEX integrator.
"""
function create_parallel_imex(pdomain::ParallelDomain, n_local::Int,
                             implicit_matrix::DistributedNSMatrix)
    
    # Use RK4 for explicit part
    explicit_integrator = create_parallel_rk4(pdomain, n_local)
    
    # Create GMRES solver for implicit part
    implicit_solver = create_parallel_gmres(30, 100, 1e-6)
    
    # Working storage
    explicit_rhs = create_distributed_vector(zeros(Float64, n_local), pdomain)
    implicit_rhs = create_distributed_vector(zeros(Float64, n_local), pdomain)
    
    timer = create_parallel_timer(pdomain.mpi_ctx)
    
    return ParallelIMEX(
        explicit_integrator, implicit_solver, pdomain,
        explicit_rhs, implicit_rhs, implicit_matrix, timer
    )
end

"""
    parallel_imex_step!(integrator::ParallelIMEX, u::DistributedVector,
                       explicit_rhs_fn, implicit_rhs_fn, dt::Float64, t::Float64)

Perform one IMEX time step.
"""
function parallel_imex_step!(integrator::ParallelIMEX, u::DistributedVector,
                           explicit_rhs_fn, implicit_rhs_fn, dt::Float64, t::Float64)
    
    start_timer!(integrator.timer, "imex_step")
    
    dt_sync = synchronize_timestep(integrator.explicit_integrator, dt)
    
    # Step 1: Explicit step for non-stiff terms
    start_timer!(integrator.timer, "explicit_step")
    u_explicit = create_distributed_vector(copy(u.local_values), integrator.pdomain)
    parallel_timestep!(integrator.explicit_integrator, u_explicit, explicit_rhs_fn, dt_sync, t)
    stop_timer!(integrator.timer, "explicit_step")
    
    # Step 2: Implicit step for stiff terms
    start_timer!(integrator.timer, "implicit_step")
    
    # Compute implicit RHS at current time
    implicit_rhs_fn(integrator.implicit_rhs.local_values, u.local_values, t)
    
    # Set up implicit system: (I - dt*J)*u_new = u_old + dt*f_impl
    # Where J is the Jacobian matrix
    implicit_system_rhs = create_distributed_vector(copy(u.local_values), integrator.pdomain)
    axpy!(dt_sync, integrator.implicit_rhs.local_values, implicit_system_rhs.local_values)
    
    # Solve implicit system
    u_new = create_distributed_vector(copy(u.local_values), integrator.pdomain)
    converged = solve!(u_new, integrator.implicit_solver, 
                      integrator.implicit_matrix, implicit_system_rhs)
    
    if !converged
        @warn "Implicit solve did not converge at time $t"
    end
    
    stop_timer!(integrator.timer, "implicit_step")
    
    # Step 3: Combine explicit and implicit contributions
    # This is simplified - real IMEX schemes have specific combination rules
    u.local_values .= 0.5 .* u_explicit.local_values .+ 0.5 .* u_new.local_values
    
    stop_timer!(integrator.timer, "imex_step")
    
    return dt_sync
end

"""
    ParallelAdaptiveTimestepper

Adaptive time stepping with parallel error estimation and step control.
"""
mutable struct ParallelAdaptiveTimestepper
    base_integrator::ParallelTimeIntegrator
    embedded_integrator::ParallelTimeIntegrator  # Lower order for error estimation
    
    # Adaptive parameters
    tolerance::Float64
    safety_factor::Float64
    min_factor::Float64
    max_factor::Float64
    
    # Error estimation
    error_norm::Float64
    previous_dt::Float64
    rejected_steps::Int
    accepted_steps::Int
    
    # PI controller parameters (for smooth time step evolution)
    pi_control::Bool
    alpha::Float64      # Proportional gain
    beta::Float64       # Integral gain
    previous_error::Float64
    
    timer::ParallelTimer
end

"""
    create_parallel_adaptive_stepper(pdomain::ParallelDomain, n_local::Int;
                                   tolerance::Float64=1e-4,
                                   pi_control::Bool=true) -> ParallelAdaptiveTimestepper

Create parallel adaptive time stepper with embedded RK methods.
"""
function create_parallel_adaptive_stepper(pdomain::ParallelDomain, n_local::Int;
                                        tolerance::Float64=1e-4,
                                        pi_control::Bool=true)
    
    # Use RK4 as main integrator and RK3 as embedded (lower order)
    base_integrator = create_parallel_rk4(pdomain, n_local)
    embedded_integrator = create_parallel_rk4(pdomain, n_local)  # Simplified - would be RK3
    
    timer = create_parallel_timer(pdomain.mpi_ctx)
    
    return ParallelAdaptiveTimestepper(
        base_integrator, embedded_integrator,
        tolerance, 0.9, 0.1, 5.0,
        0.0, 0.01, 0, 0,
        pi_control, 0.7, -0.4, 0.0,
        timer
    )
end

"""
    adaptive_parallel_step!(stepper::ParallelAdaptiveTimestepper, u::DistributedVector,
                          rhs_function, dt::Float64, t::Float64) -> Tuple{Float64, Bool}

Perform one adaptive time step with error control and step size adjustment.
Returns (actual_dt_used, step_accepted).
"""
function adaptive_parallel_step!(stepper::ParallelAdaptiveTimestepper, u::DistributedVector,
                                rhs_function, dt::Float64, t::Float64)
    
    start_timer!(stepper.timer, "adaptive_step")
    
    dt_try = dt
    max_attempts = 5
    attempts = 0
    
    while attempts < max_attempts
        attempts += 1
        
        # Take step with main integrator
        u_main = create_distributed_vector(copy(u.local_values), stepper.base_integrator.pdomain)
        dt_used = parallel_timestep!(stepper.base_integrator, u_main, rhs_function, dt_try, t)
        
        # Take step with embedded (lower order) integrator
        u_embedded = create_distributed_vector(copy(u.local_values), stepper.embedded_integrator.pdomain)
        parallel_timestep!(stepper.embedded_integrator, u_embedded, rhs_function, dt_used, t)
        
        # Compute error estimate
        error_vec = create_distributed_vector(copy(u_main.local_values), stepper.base_integrator.pdomain)
        axpy!(-1.0, u_embedded.local_values, error_vec.local_values)
        
        error_norm = distributed_norm(error_vec.local_values, 2, stepper.base_integrator.pdomain.mpi_ctx)
        stepper.error_norm = error_norm
        
        # Check if step is acceptable
        if error_norm <= stepper.tolerance
            # Accept step
            u.local_values .= u_main.local_values
            stepper.accepted_steps += 1
            
            # Compute new step size
            if stepper.pi_control
                # PI controller for smooth step size evolution
                dt_new = compute_pi_controller_stepsize(stepper, dt_used, error_norm)
            else
                # Standard step size control
                factor = stepper.safety_factor * (stepper.tolerance / error_norm)^(1.0 / (stepper.base_integrator.order + 1))
                factor = clamp(factor, stepper.min_factor, stepper.max_factor)
                dt_new = dt_used * factor
            end
            
            stepper.previous_dt = dt_used
            stepper.previous_error = error_norm
            
            if is_root(stepper.base_integrator.pdomain.mpi_ctx)
                @debug "Adaptive step accepted: dt=$dt_used, error=$error_norm, next_dt=$dt_new"
            end
            
            stop_timer!(stepper.timer, "adaptive_step")
            return dt_new, true
        else
            # Reject step and reduce step size
            stepper.rejected_steps += 1
            
            factor = stepper.safety_factor * (stepper.tolerance / error_norm)^(1.0 / (stepper.base_integrator.order + 1))
            factor = clamp(factor, stepper.min_factor, 1.0)  # Don't increase after rejection
            dt_try = dt_try * factor
            
            if is_root(stepper.base_integrator.pdomain.mpi_ctx)
                @debug "Adaptive step rejected: dt=$dt_try, error=$error_norm, reducing to $dt_try"
            end
        end
    end
    
    # If we get here, all attempts failed
    @error "Adaptive time stepping failed after $max_attempts attempts"
    stop_timer!(stepper.timer, "adaptive_step")
    return dt_try, false
end

"""
    compute_pi_controller_stepsize(stepper::ParallelAdaptiveTimestepper, 
                                  dt_current::Float64, error_current::Float64) -> Float64

Compute new step size using PI controller for smooth evolution.
"""
function compute_pi_controller_stepsize(stepper::ParallelAdaptiveTimestepper,
                                      dt_current::Float64, error_current::Float64)
    if stepper.previous_error > 0.0
        # PI controller formula
        factor = (stepper.tolerance / error_current)^stepper.alpha *
                 (stepper.previous_error / error_current)^stepper.beta
    else
        # First step or previous error was zero
        factor = (stepper.tolerance / error_current)^stepper.alpha
    end
    
    factor = clamp(factor, stepper.min_factor, stepper.max_factor)
    return dt_current * stepper.safety_factor * factor
end

"""
    get_adaptive_stepping_stats(stepper::ParallelAdaptiveTimestepper) -> Dict

Get statistics about adaptive time stepping performance.
"""
function get_adaptive_stepping_stats(stepper::ParallelAdaptiveTimestepper)
    total_steps = stepper.accepted_steps + stepper.rejected_steps
    
    return Dict(
        "accepted_steps" => stepper.accepted_steps,
        "rejected_steps" => stepper.rejected_steps,
        "total_attempts" => total_steps,
        "acceptance_rate" => total_steps > 0 ? stepper.accepted_steps / total_steps : 0.0,
        "current_error" => stepper.error_norm,
        "previous_dt" => stepper.previous_dt,
        "pi_control_enabled" => stepper.pi_control
    )
end

# Export public interface
export ParallelTimeIntegrator, ParallelRungeKutta, ParallelIMEX
export create_parallel_rk4, create_parallel_imex
export parallel_timestep!, parallel_imex_step!
export ParallelAdaptiveTimestepper, create_parallel_adaptive_stepper
export adaptive_parallel_step!, get_adaptive_stepping_stats
export synchronize_timestep